An Optimization of Multi-product Assembly Lines Using Simulation and Multi-Objective Programming Approach

This paper investigates unreliable multi-product assembly lines with mixed (serial-parallel) layout model in which machines failures and repairing probabilities are considered. The aim of this study is to develop a multi-objective mathematical model consisting the maximization of the throughput rate of the system and the minimization of the total cost of reducing mean processing times and the total buffer capacities with respect to the optimal values of the mean processing time of each product in each workstation and the buffer capacity between workstations. For this purpose, in order to configure the structure of the mathematical model, Simulation, Design of Experiments and Response Surface Methodology are used and to solve it, the meta-heuristic algorithms including Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Non-Dominated Ranked Genetic Algorithm (NRGA) are implemented. The validity of the multi-objective mathematical model and the application of the proposed methodology for solving the model is examined on a case study. Finally, the performance of the algorithms used in this study is evaluated. The results show that the proposed multi-objective mathematical model is valid for optimizing unreliable production lines and has the ability to achieve optimal (near optimal) solutions in other similar problems with larger scale and more complexity.IntroductionA production line consists of a sequence of workstations, in each of which parts are processed by machines. In this setup, each workstation includes a number of similar or dissimilar parallel machines, and a buffer is placed between any two consecutive workstations. In production lines, the buffer capacity and processing time of machinery have a significant impact on the system's performance. The presence of buffers helps the system to maintain production despite possible conditions or accidents, such as machinery failure or changes in processing time. Previous research has investigated production lines without any possibility of machinery failure, referred to as "safe production lines." However, in real production lines, machinery failure is inevitable. Therefore, several studies have focused on "uncertain production lines,"assuming the existence of a probability of failure in a deterministic or exponential distribution. This research examines uncertain production lines with a combined layout, resulting from the combination of parallel deployment of machines within each workstation, if necessary, and serial deployment of workstations. The objective of this research is to determine the optimal values (or values close to optimal) of the average processing time of each product in each workstation, as well as the volume of buffers, as decision variables. The approach aims to maximize the system's output while minimizing the costs associated with reducing the processing time of workstations and minimizing the total volume of buffers between stations. Moreover, simulation can be applied without interrupting the production line or consuming significant resources. In this research, due to the high cost and time involved, implementing the proposed changes on the system is not cost-effective for investigating the changes in the production system's output rate. Therefore, the simulation technique has been utilized to optimize the production line.Research methodThe present study aims to develop a multi-objective mathematical model, based on simulation, to optimize multi-product production lines. In the first step, the structure of the multi-objective mathematical model is defined, along with the basic assumptions. To adopt a realistic approach in the model structure, the simulation technique has been employed to address the first objective function, which is maximizing the output rate of the production line. To achieve this, the desired production system is simulated. The design of experiments is used to generate scenarios for implementation in the simulated model, and the response surface methodology is utilized to analyze the relationship between the input variables (such as the average processing time of each product type in each workstation and the buffer volume between stations) and the response variable (production rate).ResultsTo implement the proposed methodology based on the designed multi-objective programming model, a case study of a three-product production line with 9 workstations and 8 buffers was conducted. Subsequently, to compare the performance of the optimization algorithms, five indicators were used: distance from the ideal solution, maximum dispersion, access rate, spacing, and time. For this purpose, 30 random problems, similar to the mathematical model of the case study, were generated and solved. Based on the results obtained, both algorithms exhibited similar performance in all indices, except for the maximum dispersion index.ConclusionsIn this article, the structure of a multi-objective mathematical model was sought in uncertain multi-product production lines with the combined arrangement of machines in series-parallel (parallel installation of machines in workstations if needed and installation of workstations in series). The objective was to determine the optimal values of the average processing time of each type of product in each workstation and the buffer volume of each station, with the goals of maximizing the production rate, minimizing the costs resulting from reducing the processing time, and the total volume of inter-station buffers simultaneously. To investigate the changes in the output rate of the production system, due to the high cost and time, it was deemed not cost-effective to implement the proposed changes on the system. Therefore, the combination of simulation techniques, design of experiments, and response surface methodology was used to fit the relevant metamodel. In the proposed approach of this research, taking a realistic view of production line modeling, the probability of machinery failure, as well as the possibility of repairability and return to the system, were considered in the form of statistical distribution functions. Additionally, all time parameters, including the arrival time between the parts, the start-up time of all the machines, the processing time, the time between two failures, and the repair time of the machines, were non-deterministic and subject to statistical distributions. Finally, to solve the structured mathematical model, two meta-heuristic algorithms (NSGA-II) and (NRGA) were considered